Arithmetic and geometric progressions; insertion of arithmetic and geometric means between two given numbers; relation between AM and GM; sum up to n terms of special series — Sn, Sn^2, Sn^3; arithmetico-geometric progression.
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Q1 · Sequences and Series · EASY
If the sum of the first n terms of an arithmetic progression is given by Sn = 3n² + 5n, then the 10th term of the progression is:
Q2 · Sequences and Series · MEDIUM
The arithmetic mean of two numbers is 34 and their geometric mean is 16. The two numbers are:
Q3 · Sequences and Series · MEDIUM
If the sum of the first n natural numbers is equal to 8 times the sum of the first k natural numbers, where n = 4k, then the value of k is:
Q4 · Sequences and Series · MEDIUM
The sum of the series 1×2 + 2×3 + 3×4 + ... + n(n+1) is equal to:
Q5 · Sequences and Series · HARD
Let a, b, c be in geometric progression with common ratio r > 1. If the arithmetic mean of a and c exceeds b by 3/2, and a + b + c = 21, then the value of a is: